Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;


public class A {
    public static void main(String[] args) throws Exception {
        new A().solve();
    }
    void solve() throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(in.readLine());

        long[] T = new long[1000000];
        int size = 0;
        for (long k = 1; (k * (k + 1)) / 2 < 1000000000; k++) {
            T[size++] = (k * (k + 1)) / 2;
        }

        int up = size - 1, low = 0;
        while (low <= up) {
            long v = T[low] + T[up];
            if (v < n) {
                low++;
            } else if (n < v) {
                up--;
            } else {
                System.out.println("YES");
                return;
            }
        }
        System.out.println("NO");
    }
}